gistfile1.js

var arr = [2,4,1,4,1,2],

    min = function(values){ return Math.min.apply(null, values); },
    max = function(values){ return Math.max.apply(null, values); },

    minValue = min(arr),
    maxValue = max(arr),
    
    extremeIdxsOfMinValue = [arr.indexOf(minValue), arr.lastIndexOf(minValue)],
    extremeIdxsOfMaxValue = [arr.indexOf(maxValue), arr.lastIndexOf(maxValue)],

    minIdxOfMinValue = min(extremeIdxsOfMinValue),
    maxIdxOfMinValue = max(extremeIdxsOfMinValue),
    minIdxOfMaxValue = min(extremeIdxsOfMaxValue),
    maxIdxOfMaxValue = max(extremeIdxsOfMaxValue),

    leftIdx = min([minIdxOfMinValue, maxIdxOfMinValue, minIdxOfMaxValue, maxIdxOfMaxValue]),
    rightIdx = max([minIdxOfMinValue, maxIdxOfMinValue, minIdxOfMaxValue, maxIdxOfMaxValue]);

    if(~[minIdxOfMinValue, maxIdxOfMinValue].indexOf(leftIdx) && ~[minIdxOfMinValue, maxIdxOfMinValue].indexOf(rightIdx)){
        rightIdx = maxIdxOfMaxValue;
    } 

    if(~[minIdxOfMaxValue, maxIdxOfMaxValue].indexOf(leftIdx) && ~[minIdxOfMaxValue, maxIdxOfMaxValue].indexOf(rightIdx)){
        rightIdx = maxIdxOfMinValue;
    }

var sum = arr.slice(leftIdx,rightIdx+1).reduce(function(acc, el){
    return acc+el;
}, 0);

var product = arr.slice(0, leftIdx).concat(arr.slice(rightIdx+1)).reduce(function(acc,el){
    return acc*el;
}, 1)

console.log(sum, product);